De-quan Yu, He Huang, Gunnar Nyman, Zhi-gang Sun. Hermiticity of Hamiltonian Matrix using the Fourier Basis Sets in Bond-Bond-Angle and Radau Coordinates[J]. Chinese Journal of Chemical Physics , 2016, 29(1): 112-122. doi: 10.1063/1674-0068/29/cjcp1507141
Citation: De-quan Yu, He Huang, Gunnar Nyman, Zhi-gang Sun. Hermiticity of Hamiltonian Matrix using the Fourier Basis Sets in Bond-Bond-Angle and Radau Coordinates[J]. Chinese Journal of Chemical Physics , 2016, 29(1): 112-122. doi: 10.1063/1674-0068/29/cjcp1507141

Hermiticity of Hamiltonian Matrix using the Fourier Basis Sets in Bond-Bond-Angle and Radau Coordinates

doi: 10.1063/1674-0068/29/cjcp1507141
  • Received Date: 2015-07-04
  • Rev Recd Date: 2015-07-13
  • In quantum calculations a transformed Hamiltonian is often used to avoid singularities in a certain basis set or to reduce computation time. We demonstrate for the Fourier basis set that the Hamiltonian can not be arbitrarily transformed. Otherwise, the Hamiltonian matrix becomes non-hermitian, which may lead to numerical problems. Methods for correctly constructing the Hamiltonian operators are discussed. Specific examples involving the Fourier basis functions for a triatomic molecular Hamiltonian (J=0) in bond-bond angle and Radau coordinates are presented. For illustration, absorption spectra are calculated for the OClO molecule using the time-dependent wavepacket method. Numerical results indicate that the non-hermiticity of the Hamiltonian matrix may also result from integration errors. The conclusion drawn here is generally useful for quantum calculation using basis expansion method using quadrature scheme.
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Hermiticity of Hamiltonian Matrix using the Fourier Basis Sets in Bond-Bond-Angle and Radau Coordinates

doi: 10.1063/1674-0068/29/cjcp1507141

Abstract: In quantum calculations a transformed Hamiltonian is often used to avoid singularities in a certain basis set or to reduce computation time. We demonstrate for the Fourier basis set that the Hamiltonian can not be arbitrarily transformed. Otherwise, the Hamiltonian matrix becomes non-hermitian, which may lead to numerical problems. Methods for correctly constructing the Hamiltonian operators are discussed. Specific examples involving the Fourier basis functions for a triatomic molecular Hamiltonian (J=0) in bond-bond angle and Radau coordinates are presented. For illustration, absorption spectra are calculated for the OClO molecule using the time-dependent wavepacket method. Numerical results indicate that the non-hermiticity of the Hamiltonian matrix may also result from integration errors. The conclusion drawn here is generally useful for quantum calculation using basis expansion method using quadrature scheme.

De-quan Yu, He Huang, Gunnar Nyman, Zhi-gang Sun. Hermiticity of Hamiltonian Matrix using the Fourier Basis Sets in Bond-Bond-Angle and Radau Coordinates[J]. Chinese Journal of Chemical Physics , 2016, 29(1): 112-122. doi: 10.1063/1674-0068/29/cjcp1507141
Citation: De-quan Yu, He Huang, Gunnar Nyman, Zhi-gang Sun. Hermiticity of Hamiltonian Matrix using the Fourier Basis Sets in Bond-Bond-Angle and Radau Coordinates[J]. Chinese Journal of Chemical Physics , 2016, 29(1): 112-122. doi: 10.1063/1674-0068/29/cjcp1507141
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